$7\mathrm{.}4-12$ An arm $\backslash ($ A B C $\backslash )$ lying in a horizontal plane and supported at $\backslash ($ A $\backslash )($see figure$)$ is made of two identical solid steel bars $\backslash ($ A B $\backslash )$ and $\backslash ($ B C $\backslash )$ welded together at a right angle. Each bar is $0\mathrm{.}5$ m long.

Knowing that the maximum tensile stress $($principal stress$)$ at the top of the bar at support $\backslash ($ A $\backslash )$ due solely to the weights of the bars is $6\mathrm{.}5$ MPa $,$ determine the diameter $\backslash ($ d $\backslash )$ of the bars.

PROB. $7\mathrm{.}4-12$